Do you have questions about what your child is learning in mathematics? To learn more about the Kindergarten Math Standards, check out the video below.

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**What is direct modeling?**

Direct modeling is when students show exactly what is happening in the problem, using manipulatives or pictures, to solve. Direct modeling is a powerful strategy that provides a foundation for the more advanced strategies that follow.

**When should direct modeling be used?**

The first step in developing a student’s understanding of a new math concept should be for them to directly model problems. If you don’t have the ability to model a problem, you cannot solve the problem. When a student struggles with a math problem, avoid referring to the operation (addition, subtraction, multiplication or division). Students who are struggling should be reminded to think about what is happening in the story and find a way to show it. As children grow in their sophistication, they will no longer need to and should not be expected to directly model every problem. Most students will directly model problems they find challenging, which should be encouraged.

**What skills are improved through direct modeling?**

Direct modeling supports student’s ability to contextualize and decontextualize. When students directly model a problem, they are contextualizing parts of the problem in order to show what is happening. For example, in the task “There are 8 bags of cookies with the same amount of cookies in each bag. If there are 48 cookies, how many cookies are in each bag?” students are expected to identify that 8 represents the number of cookie bags, 48 represents the number of cookies, and that it is unknown how many cookies are in each bag. While students directly model the problem, they should label what their manipulatives or picture represent. The ability to identify the meaning of the numbers in the problem will increase problem solving skills.

Strong direct modeling skills will also lead to student’s ability to decontextualize a problem. This means that they will be able to translate a task into numbers and symbols. Using the task in the previous paragraph, students who can decontextualize will be able to translate the situation in the equations: 8 x ____ = 48 or 48/8 = _____ and then solve the task. Why aren’t we decontextualizing the problem as ___ x 6 = 48? Many times we hear: What does it matter? You get the same answer anyways? Although we know that 8 x 6 = 48 and 6 x 8 = 48, the first equation matches what is happening in the problem, the second one does not. It is important that when we decontextualize we are still keeping in mind what we know about direct modeling.

To view a student directly model a problem, watch this video from McGraw-Hill.

For more examples of how different addition and subtraction problem types are directly modeled, visit this link.

**What are the benefits of homework?**

• Students: deepens understanding and solidifies concepts learned in class.

• Parents: communicates what students are learning; an opportunity for parents to help their child.

• Teachers: provides feedback about what students have previously learned; helps guide instructional decisions

**Below are the guidelines for elementary school homework listed in the Hillsborough County Public Schools Student Handbook. **

**Important highlights of the homework guidelines include:**

• Homework should not cover new concepts; it should reinforce concepts already learned.

• In 4th grade, homework for all subject areas should not exceed a total of 45 minutes.

• Homework should not impact math report card grades; it should be reflected in “Expected Behaviors” section of the report card.

• Homework can be differentiated.

• Regular feedback about homework should be given to parents.

• Students should be able to accomplish the homework on their own.

**What could 4th grade math homework look like?**

• 1-2 problems (teacher created, or taken from a Go Math resource, Item Specifications, or a unit homework flyer) which require that students explain their thinking with models, words and numbers.

• Active thinking with a multiple choice question; students explain why all of the solutions not chosen are incorrect. This may also include multi-select questions with more than one correct answer.

• Process questions in which the answer is already given, and the importance is placed on finding different ways to justify the answer.

• A game that has already been played in class, sent home to play with older sibling or parent.

To assist with the implementation of purposeful homework, a sample homework sheet has been created for every grade level, one sample per unit. The purpose of the homework sheet is to encourage discussion about math concepts between both the parent and child, and the parent and teacher. There is also a template included in each unit; teachers are encouraged to continue that same format of homework for other concepts within a unit. These samples can be accessed on page 1 of each unit of study. A sample homework sheet is shown below:

Parent flyers have also been created for each K-5 math unit to communicate student learning with parents. The flyers include information about the content, sample tasks, a video, and purposeful practice tasks that parents can implement with their child at home. Flyers can be printed out and sent home, or parents can access the flyer for each unit at http://www.sdhc.k12.fl.us/doc/list/elementary-mathematics/resources/78-291/.

Additional information on homework, specifically ways parents can support at home can be found at http://alturl.com/rax3q or at https://youtu.be/-f0eC136F-k

The 4th Grade FSA Item Specifications, found at http://fsassessments.org/wp-content/uploads/2015/08/Grade-4-Math-Test-Item-Specifications_Final_May-2016.pdf, can be a useful resource for homework sample problems and item types.

“I spy an object that is below the television…”

“I spy an object that is under the window…”

Simon says, “Stand next to your chair…”

Simon says, “Hold the ball over your head…”

Simon says, “Put the pattern blocks on top of your desk…”

“I spy” and “Simon Says” are not only fun games to play with Kindergarten students during the first weeks of school, but they are also a wonderful task to practice using positional words. MAFS.K.G.1.1 states that students should, “Describe objects in the environment using names of shapes, and describe the relative position of these objects using terms such as above, below, beside, in front of, behind, next to.” Using common games such as, “Simon Says, and I spy” allows students opportunities to use positional vocabulary when describing objects in a game fashion. This skill will be useful as students apply their understanding of positional words in later units.

These games can be played during the Math Block, Teacher Directed P.E., Brain Breaks and moving about the building to and from lunch. Consider incorporating tasks similar to “I Spy” and “Simon Says” to practice describing objects using positional words.

**What is Place Value?**

Place Value is the value of a digit in a number based on the location of the digit. Place Value understanding is essential for students to add and subtract multi-digit numbers. Students need to understand that the place value system we use is in base ten is comprised of ones, tens, hundreds and thousands.

In 3rd grade, students are expected to:

• Use place value understanding to round whole numbers to the nearest 10 or 100.

• Fluently add and subtract within 1,000, using strategies and algorithms based on place value.

• Multiply one-digit whole numbers by multiples of 10 in the range of 10-90 using strategies based on place value.

**How can we strengthen students’ understanding of place value?**

Using place value to represent numbers is an important skill that students will need in order to add and subtract using place value understanding and vocabulary.

**Here are different ways to explore and represent numbers ruing place value:**

1. Base ten models – Students are given tasks to explore and understand representing numbers with base ten blocks and later move to drawing quick picture representations of these numbers. This helps them understand what a number is comprised of. A place value chart can be utilized with these models.

Typically the exploration with these tools begins by handing a unit (ones), rod (tens), flat (hundreds), and a cube (thousands) and posing the question, “How do these tools relate?” Through exploration, you want students to realize that it takes ten units to make a rod (ten ones to make a ten), ten rods make a flat (ten tens make a hundred) and ten flats make a cube (ten hundreds make a thousand).

2. Expanded Form – Representing numbers based on the value of each digit in a number. For example 417 in expanded form is 400 + 10 + 7 based on the location of each digit. You want to continue making this process hands-on by using number stack-up cards.

3. Base ten language – Using place value language to identify what each digit’s value is. For example 582 is worth 5 hundreds, 8 tens and 2 ones.

4. Word Form – Important to have students use and understand place value vocabulary. Record numbers in word form exactly as you say them out-loud, such as 936 as “nine hundred thirty-six.”

5. It could also help to create an anchor chart with the different representations and place value language. Keep referring students to the anchor chart when discussing, writing and representing numbers with place value language.

6. Representing numbers flexibly is another essential strategy students learned in 2nd grade, which help with developing a deeper understanding of number and place value. For example: 316 can be represented as 3 hundreds, 1 ten and 6 ones OR 2 hundreds, 11 tens and 6 ones. This is not a specified strategy in the 3rd grade standards, but you may want to keep it in mind as students are representing numbers and applying invented strategies when adding and subtracting.

**When should we be building place value understanding?**

The Building Math Community during the first 9 days is a great time to reinforce place value concepts students learned in 2nd grade so they will be ready to apply the understanding of number to addition/subtraction concepts. Place Value centers and morning work are also great opportunities to spiral review and reinforce these place value concepts and continue to connect to upcoming units/concepts.

Make sure to post and make visible the place value language and models you want your students to utilize while building understanding of place value.

For great free printable resources to explore expanded form in a hands-on exploration with stackable number cards, visit the website http://goo.gl/9112KJ.

Another great resource for composing and decomposing numbers into expanded form or standard form is https://illuminations.nctm.org/Lesson.aspx?id=3691 from NCTM Illuminations.

**What are open number lines?**

An open number line starts as a line with no numbers. They can be used as a visual representation for recording thinking during the process of mental computation.

**Why are open number lines so useful?**

Open number lines are a great tool to get students to move past manipulatives to representing their thinking on paper. Using this strategy will increase students’ confidence in their ability to use numbers flexibly which will lead to stronger number sense. Using them will also help students who are not ready for the algorithm yet, but will shrink the gap because of the number sense it builds. Open number lines can be used by students to represent their thinking with many different concepts, including addition, subtraction, multiplication, division, and elapsed time. Open number lines are less time consuming than waiting for students to record all the numbers on a 0-100 ranged number line. It is also useful that the space between lines do not need to be precise on an open number line. It’s truly about using a tool to help you understand and think through a problem.

**How do I get students to use open number lines?**

To expose students to open number lines, it is great to start with a pre-made concrete example that they can explore and discuss. It is also helpful to use questioning to encourage a student to try the strategy while the class is problem solving. Have that student share their open number line with the class. It always works best if the teacher is very excited about this new strategy and records the example on an anchor chart. Challenge all students to use an open number line when working on their next problem(s).

**What resources are available?**

Open number lines can be drawn on white boards and in math journals. There are also resources available that could be cut and laminated for students to use, including this one.

This video has students demonstrating how to use an open number line. For more information on open number lines, Marilyn Burns explains how she uses them when subtracting with students on her blog.

There is also an Open Number Line Mini PDM located in the Mini PDM folder on our IDEAS Elementary Math Bulletin board.

**Anchor charts are essential to the math classroom. These simple posters help students take their thinking to the next level. Here are 7 reasons why anchor charts are incredible!**

1. Math anchor charts provide a source of visual reference to support students’ thinking, reasoning, and problem solving. Whenever your students are learning something that they may need to refer back to later in the lesson, the week, the unit or even later in the year, it is a great idea to make an anchor chart. You may not even have planned to make an anchor chart in a lesson, but if you see that thinking is happening that needs to be recorded, it may pay-off to make one.

2. Anchor charts help students recognize the learning goal. As the students get closer to reaching the learning goal, they can use the anchor chart to scaffold their understanding.

3. They support and develop precise math language, because students can reference them when writing and discussing their thinking.

4. When students are a part of the creation of the anchor chart, their buy-in increases exponentially. Students are more likely to reference the anchor chart if their thinking and ideas are displayed. As students make discoveries that support the learning goal during the math lesson, include them on the anchor chart.

5. They can be used to make connections between new content and previously learned content. Always keep anchor charts accessible throughout the year so students can refer back to them when making connections.

6. Anchor charts build confidence in ESE and ELL students. When a chart is created that targets all learners, students who need the extra support will utilize it to increase their understanding.

7. Artistry is not important when it comes to anchor charts. Although it is best if the writing is legible and the thinking is organized, it does not need to look like a Pinterest anchor chart to be useful. Sometimes, as thinking is added to the chart during class, it does become too messy. A quick-fix for that is to re-write it after school, so the students will be able to reference their previous thinking on a more organized anchor chart. Thankfully, all of us non-artists can make awesome anchor charts, too!

Check out these links for additional information: http://www.k-5mathteachingresources.com/Math-Anchor-Charts.html and http://www.weareteachers.com/blogs/post/2015/11/12/anchor-charts-101

It’s important in grade 5 for students to have a solid understanding of multi-digit multiplication. One way to do that is to make connections between methods. Take for example, the traditional method and the partial products method. Let’s learn a little about each method.

The partial products method consists of all the individual products produced by the multiplication being recorded on separate lines then added. The partial products method can be useful and help students better understand the traditional method which is probably how most of us learned how to multiply.

The traditional method is a version of the partial products method. In the traditional method, some of the partial products are added mentally before the sum is written down. In some instances, the traditional method is more efficient than the partial products method (because it requires less writing). But this method is not as easy to understand step by step and it may be more susceptible to error (because steps are combined and done mentally).

So you’re probably wondering how do I connect these two methods for children?

One way is to use the distributive or break apart strategy. The distributive property helps children understand the relationship between the traditional method and the partial products method. Take our example, 365 x 27, fifth graders should readily think that it could be computed by (365 x 20) + (365 x 7) or in the example 356 x 9 they think (300 x 9) + (50 x 9) + (6 x 9).

Here are some guiding questions to your support your child’s thinking:

Where do you see the partial products recorded in the traditional method?

Why do I add the partial products?

How could you solve 49 x 58 using both methods?

**What are Math Norms?**

Math Norms are a set of expectations that describe what should be occurring in the classroom during math instruction. Norms should be written in a positive manner and outline student and teacher actions. Norms should cover how to engage in tasks such as: Using tools to solve problems, communicating thinking, and showing student work. Norms should be written in kid friendly language and clearly posted in the classroom for both student and teacher reference.

**Why use Math Norms?**

Kindergarten students need explicit modeling of how to engage in a mathematics lesson. Norms provide clear, positive, and achievable expectations for how both the students and teachers will act in the math classroom. Setting norms will show students how to become an active part of the classroom thus increasing classroom culture.

**When do I introduce Math Norms?**

Math norms should be introduced during the first weeks of school. The Kindergarten Instructional Guides provides opportunities during the first 9 days of instruction to establish and practice Math Norms. You might want to take pictures of students engaging in the Math Norm and post them next to the Math Norms as a visual reminder of the expectations. It is important that you continue practicing these Math Norms throughout the school year.

**What are some examples of Math Norms I could use? **

1. Explain your thinking

2. Ask questions

3. Challenge ideas, not classmates (peers)

4. Say when I don’t understand or agree

5. Actively participate in all learning tasks

6. Choose and use math tools appropriately

7. Show your work in more than one way

8. When a classmate is sharing, be prepared to respond with how you agree,

disagree or ask a question (Actively Listen)

9. Be Respectful when you agree/disagree with someone

Work with your students to create 3-5 norms that outline the Math Behaviors you would like to see in your classroom. It is important to explicitly practice those Math Norms so that all stakeholders are aware of the expectations.

For more information on Math Learning Environments, read the article below

http://www.nctm.org/Publications/teaching-children-mathematics/2011/Vol17/Issue8/A-reflective-protocol-for-mathematics-learning-environments/

**What are the benefits of homework?**

• Students – homework deepens their understanding and solidifies concepts learned in class.

• Parents – homework communicates what students are learning. It’s also an opportunity for parents to help their child.

• Teachers – homework gives teachers feedback about what students have previously learned. It also helps guide decisions about what math instruction students need.

**Below are the guidelines for elementary school homework listed in the Hillsborough County Public Schools Student Handbook. **

**Important highlights of the homework guidelines include:**

• Homework should not be new concepts, it should reinforce concepts already learned.

• In 3rd grade, homework should not exceed 30 minutes a night, including all subject areas.

• Homework should not be counted toward math grade, instead should be reflected in Expected behaviors section of the report card.

• Homework can be differentiated.

• Regular feedback should be given about the homework to parents.

• Students should be able to accomplish the homework on their own.

**What could 3rd grade math homework look like?**

• 1-2 problems taken from Think Central, a Go Math resource, Item Specifications, sample unit homework flier or teacher created, where students explain their thinking with models, words and numbers.

• Active thinking with a multiple choice question, where students record why all the solutions not chosen are incorrect. This may also include multi-select questions with more than one correct answer.

• Process questions where the answer may already be given, the importance is on finding different ways to solve the problem.

• Game already played in class, then sent home to play with older sibling or parent.

• Should include real-world problem solving scenarios.

**How important is teacher-parent communication in the homework process?**

As a parent, it is important to establish timely and clear communication with your child’s teacher. Here are some questions you may want to consider asking the teacher to start the discussion:

• What are the upcoming topics in math?

• What math topic causes my child the most difficulty?

• How could I best support what is happening in the classroom?

**Additional questions about math homework:**

• Should my child be able to complete the homework on their own?

• I’m worried about why my child can’t finish the problems. What might we do to help him?

• If my child is struggling with homework, how should I communicate this to you?

• How does my child receive feedback about their homework?

To assist with what homework could look like, this year a sample homework sheet has been created for every grade level, one sample per unit. The purpose of the homework sheet is to encourage discussion about math concepts between both the parent and child, parent and teacher. There is also a template included in each unit, where teacher can continue that same format of homework for other concepts within a unit. These samples can be accessed on page 1 of each unit of study. A sample homework sheet is shown below:

Parent flyers have also been created for every grade level, for every unit to communicate with parents what their child will be learning. The flyers include information about the content, sample tasks, a video, and purposeful practice tasks that parents can implement with their child at home.

Flyers can be print out in paper form or the parents can access the flyer for each unit at http://www.sdhc.k12.fl.us/doc/list/elementary-mathematics/resources/78-291/.

For more information on homework for 3rd grade math, or as parents how to help your child with math, please visit: Math Homework Help Grade 3 Video http://alturl.com/kqkh2 Or YouTube: https://youtu.be/2K5CrlpMLyw.

You also may want to visit, http://goo.gl/TjSCXV, which has the FSA Item Specifications for Grade 3, with sample problems that you may want to include in your homework.

Shelley Fritz
August 7th, 2016
Math, Math Grades 3-5, Math Grades K-2, Science, Science Grades 3-5, STEM, STEM Grades 3-5
1542
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**Building vocabulary knowledge and usage in mathematics and science should not amount to copying definitions in notebooks.** Decades of copying definitions has resulted in many students being able to repeat a definition but not show its application in context. A few days or weeks after the test, that word has been forgotten. How can teachers help students retain vocabulary words and understand them in context? We can teach students how to use parts of words to help determine the meaning. Let’s use the word **perimeter** as an example. The prefix peri means around. The suffix meter refers to an instrument for measuring and recording the quantity of something.

This fence is an example of marking the perimeter around an area. Have students seek examples of words in the environment and take pictures to post on a word wall with related concepts.

Quadrilaterals can be found all around us. Have students take pictures or sketch in their notebooks or for the class word wall.

**Emphasize vocabulary through fun, engaging lessons.**

1. **What’s on my Back?** Place a label with a math or science vocabulary word on each student’s back and have them pair up to ask questions their partner can only answer yes or no to as they try to figure out what word is on their back. They can ask three questions, take notes, then move on to a new partner and ask more questions. They’ll continue until they can guess the word. They can get a new word and begin the process again. This activity builds questioning skills and encourages critical thinking.

2. **Flyswatter** Give two students flyswatters and have a third student read aloud a definition he or she has written while the two students compete to swat the word defined on the word wall. Involve more students by having them make word cards for the table and use a counter to place on the word card that matches the definition read aloud. Descriptions and definitions should be generated by the students.

3. **Remove One** Distribute one vocabulary word card to each student. Play some music as they mingle and trade cards. Stop the music and they need to form a group of four. Their mission is to find how their word is connected to the other words so that they don’t get removed from the group. Call upon each person who got removed from the group to see how their vocabulary word may connect with other words across the room. This will help students make connections among concepts and it can also reveal lack of understanding of vocabulary.

Find more ideas for building vocabulary, click here: language of math

Here are more great activities for getting students engaged in applying vocabulary knowledge: The Language IN Math

Shelley Fritz
August 6th, 2016
Math, Math Grades 3-5, Math Grades 6-8, Math Grades K-2, STEM Grades 3-5
2281
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How effective is it to have a list of math words on the wall? Who decides what words to place on the wall and who puts them up on display? Students benefit from building vocabulary knowledge. Teachers often create word walls to support reinforcement of mathematical terms. Students, especially English Language Learners (ELLs), benefit from seeing words in print with a picture as a reminder of the meaning of the word. Traditional word walls have displayed lists of words that are frequently arranged in alphabetical order across a bulletin board. At the start of the school year, many teachers have spent numerous hours building a word wall to be ready for the first day of school.

Think about why you are putting up a word wall in the first place. Is it for the purpose of learning? Consider the idea of NOT making a word wall yourself. Have your students take control of designing the classroom math word wall throughout the course of the unit. Make your word wall part of instruction by having students apply what they have learned. Their sketches and explanations can then be displayed thereby deepening their understanding of the words and reinforcing it with their drawings and words that they will remember.

Best practices in using an interactive word wall include the following:

• Academic vocabulary is posted.

• Words are visible to all students from a distance.

• Vocabulary words are aligned to current instruction.

• Student-generated material is used to create the word wall.

• Visuals are used including photographs, sketches, or actual items called realia.

• Words/visuals are arranged to show relationships among concepts.

The terms “distributive property” and “expressions” often cause confusion for students. As you plan lessons around difficult concepts, plan how and when students will internalize vocabulary through rich experiences explaining, sketching or taking pictures of the concepts modeled with math manipulatives.

You can use anchor charts created with the students during math lessons to build your word walls, too.

Find more ideas for creating successful word walls with your students by visiting Illustrative Word Wall

and

Math Word Walls

*Why teach math vocabulary?*

The Standards for Mathematics emphasize that mathematically proficient students communicate precisely to others; however, the language of mathematics can often be confusing. Lack of knowledge of math vocabulary can hinder achievement.

*What makes math vocabulary different from other subjects?*

Math vocabulary is unique in that the purpose is to communicate mathematical ideas, so it is necessary to first understand the mathematical idea the language describes. With the new understanding of the mathematical idea comes a need for the mathematical language to precisely communicate those new ideas.

*When should you teach math vocabulary?*

Introduce the vocabulary only after you have identified the vocabulary to be taught, developed your own understanding of the related math ideas, and then purposefully planned for how to connect the meaning to learning experiences.

While pre-teaching vocabulary may be appropriate for other subjects, since mathematical vocabulary represents a mathematical concept, it does not make sense to teach the word before students understand the concept. Rather, vocabulary words should be introduced to students through active engagement with the math.

Only after students have developed a conceptual understanding and expressed that understanding in their own words should the teacher help students connect the formal vocabulary with their current understanding. Introducing the vocabulary during the lesson connects it to the meaningful math they are doing at the time. It supports the math and allows them to be more precise in their justifications and explanations.

*What are some strategies for teaching math vocabulary?*

**1. Concept Attainment/Concept Card**– Having students develop their own definitions helps them focus on key characteristics of concepts, thus building conceptual understanding.

Step 1: Teacher presents students with several examples and non-examples. The teacher may choose to tell students the name of the concept, or may wait to give the formal names to the concepts until after the class has developed a final definition.

Step 2: Students consider first set of examples and non-examples and develop a rough draft of a definition. Initial definition is recorded where class can see it, and everyone has the opportunity to revise it.

Step 3: Additional pairs of examples and non-examples are presented, and with each pair, students revise their definition. Teacher uses questioning and strategically selects and orders the examples and non-examples to facilitate the refinement of the definition.

Step 4: Students create additional examples and non-examples to add to the concept card.

**2. Frayer Models-** Students identify examples and non-examples of a concept and differentiate between defining and non-defining attributes/characteristics. In an alternate version, they are developing a definition, identifying examples and non-examples, and providing an illustration or characteristics.

**3. Concept Circle/What’s my rule?/Eliminate it!** – Students describe the common attributes or name the relationship that exists between the circle in an attempt to label the circle. Students can also be given the label of the circle and asked to provide an additional example. Or, students can be given the label and the circle can include a non-example which students are asked to identify.

**4. Discussion** (Think-Pair-Share, Turn and Talk, Revoicing)- Keeping in mind the goal of precise communication, it is important that all students engage in using the new language. Using cooperative structures increase participation in the discussion and promote accountability.

**5. Journaling-** Writing about mathematics not only provides students with another opportunity to understand math language, but it also gives teachers the opportunity to assess student understanding of the terms they use.

**6. Interactive Math Word Wall**– Word walls encourage discussion and facilitate connections between the vocabulary and the mathematical ideas they represent. Here are some math word wall activities to incorporate into your daily routine:

• Pictionary – Students draw a representation of one of the words for the others to guess.

• Fly Swatter – Give the definition of a word, ask who sees the word, and give that student a fly swatter to swat the word

• I AM/Vocabulary Riddles – Students take turns saying, “I AM……” then fill in the blank using the definition for one of the words. (Ex. “I AM the answer in multiplication.”) The person who identifies the correct word is the next one to take a turn.

For more information on use of the graphic organizers, visit http://oame.on.ca/main/files/thinklit/FrayerModel.pdf

**What is differentiation in math?**

Differentiation in math is responsive teaching that stems from teachers’ understanding of how teaching and learning occurs. Differentiation is responding to varied learners’ needs for more structure or more independence, more practice or greater challenge, and more active or less active approaches to learning.

**3 main ways to differentiate:**

**1. Tools** – the manipulatives or tools students use to solve a problem can be differentiated based on their level of understanding. For example: students that are at an enrich level may want to self-select their tools, core level students may be ready to draw a quick picture, where a re-teach level student may need to have a tool suggested to help them think through a problem or task. For example: All students may play fraction war to demonstrate an understanding of comparing fractions. Re-teach level students need to prove each answer with fraction tiles, core level students can draw a number line or quick picture, enrich level students will explain how they know their fraction is greater using missing pieces.

**2. Tasks** – differentiate what problems and tasks are posed. The ultimate goal is for all students to have an understanding of the learning goal by the end of the lesson, but the way they get to that understanding may look different. A problem’s numbers can be changed to make it less/more complex or the amount of writing in the problem could be differentiated.

**3.Questions asked** – pose questions that are adjusted to the level of complexity that meets a student’s readiness level. Questions should encourage students to do more than recall known facts. Questions should have the potential to stimulate thinking and reasoning. When using questions to differentiate, teachers need to plan tiered questions anticipating what may happen throughout a lesson.

Differentiation needs to be planned for and anticipated, but the teacher should be responsive during the lesson based on their informal assessments of the students’ level of understanding. Differentiation can occur when students are independently working, working with partners, or in small groups.

**What are some ways to informally assess a student’s level of understanding?**

There are different ways to quickly informally assess student understanding throughout the lesson. The easiest way is to pose a problem/task and use one of the strategies below to record each student’s level of understanding.

• Post-it notes – place 3-4 different post-it notes on a clipboard to signify the re-teach, core and enrich groups.

• Observation checklist – record specific details about the concept and use a plus, check, minus system to determine trends of student understanding of a concept.

• Students can self-assess – have students tell you their level of understanding with a smiley face/straight face/sad face system or color coded system.

• Code student journals – as the teacher is monitoring student work, place a colored dot or star/check/circle to signify which level of understanding a student has.

• Pass out a specific shape – pass out a pattern block shape based on the student’s level of understanding. (For example: Enrich – red trapezoid, Core – green triangle, Re-teach – blue rhombus)

• Exit tickets – use exit ticket problems from the day before to determine tiered small groups for the next day’s lesson.

Small groups may play a role in differentiating the three different ways. The math small groups should be fluid and recent informal assessments done by the teacher should help guide what support each individual student needs. Many teachers use the format below to make the transitions into small groups easy for differentiation. (The writing on the chart could be labeled for each group or color coded).

**For parents:** it’s important to know that sometimes your child’s work in math may look different than another student’s. The tools, tasks, questions, and level of support offered is to address the individual needs of the instruction for your child. Students may struggle with one math concept but be strong in another, so the differentiation will be fluid.

**Teachers!!! **For more information on differentiation, please visit the math differentiation mini professional development module located on your IDEAS math bulletin board.

Also visit these websites for more information on differentiating math instruction at http://165.139.150.129/intervention/Differentiated%20Instruction%20for%20Math.pdf or http://www.davidsongifted.org/Search-Database/entry/A10513.

This school year we have some new resources linked in your Instructional Guides. In addition to the GCGs, PowerPoints, and Assessments, you will find 3 new resources, Unit Summaries, Parent Partnership Homework, and Distributed Practice to assist you as you make instructional decisions in your classroom.

Unit Summaries are linked on the Unit of Study overview page for each Unit. The Unit Summary is a resource to communicate students’ progress on their understanding of the math concepts in each unit. Each Unit Summary provides sample problem types to help parents understand how students are assessed, as well as suggested resources to help students practice math concepts at home. They can also be used to document student progress of the grade 5 Florida Standards.

Parent Partnership Homework resource can also be found on the Unit of Study overview page. This resource includes a homework task that encourages communication between home and school. There is one sample homework sheet per unit. These tasks can be used to reinforce and get feedback from parents on students previously learned concepts and to support communication between home and school.

Distributed Practice is a resource that can be found in the PowerPoint and also on the Math Icon starting in Unit 1. Distributed Practice questions cover previous grade level skills students need to be successful on current content. The data collected from Distributed Practice can help you plan lessons that meet the individual needs of your students.

Read the following blog for more information about distributed practice: http://smathsmarts.com/distributed-practice-whats-the-point/

Have you ever thought about using Five Frames to reinforce positive choices within the classroom?

The first few months of school are spent building community within the classroom. Part of building community is reinforcing positive choices. Teachers use a variety of strategies to reinforce good choices such as, individual points, table points, and classroom points. Why not practice representing numbers WHILE reinforcing positive choices.

Kindergarten students spend the first few units of school year representing numbers. As you work to build community in your classroom, consider using the Five Frame to capture the positive choices students are making. As the frames are filled, students begin to subitize numbers (see a small set of numbers and know the amount without counting). This will help students think about the relationship of numbers. This understanding helps set the foundation for understanding the number system.

Questions to ask students as you use the five frames:

1. How many squares have a counter?

2. How many squares are empty?

3. How many more are needed to make 5?

Once your students understand the five frames, you can introduce the tens frame to continue reinforcing number representations as well as positive choices.

**Do you find it difficult to get your students to talk about math? Do you feel like the quality of their discussions could improve? Here are four steps that will increase the success of accountable talk in your class!**

Step 1: Introduce accountable talk stems

Accountable talk stems are a guide for students to use as they discuss and respond to each other about their thinking, so meaningful conversation and learning can occur. Starting with a few at the beginning of the year, and adding more later on is a great way to get students to use them, without feeling overwhelmed. Make these stems visible and accessible to your students. The stems could be on cards, laminated and put on rings for students to use when having a discussion. Another idea is to have an anchor chart where they are displayed.

**Step 2: Model using the accountable talk stems**

Using another adult or a student as a discussion partner, model having a discussion using the accountable talk stems. We don’t often model in math, but modeling how to have a discussion is key to your students having success with this practice throughout the year. Modeling how to act while discussing is important as well. Looking your partner in the eye, listening, and responding with quality feedback are essential. Setting these expectations and procedures at the start of the year will lead to high level thinking and discussions taking place in your class every day.

**Step 3: Practice accountable talk with non-content related and prior grade level content questions**

If you could bring one item to a deserted island you were stuck on, what would it be and why? The beginning of the school year is a PERFECT time to practice having discussions using stems with silly questions. Not only are the students getting to practice what you have modeled with low stress questions, they are getting to know each other as fellow classmates. The first 9 days of the school year are also a great time to practice accountable talk with content from the previous grade level, as the Building Math Community resource suggests. During this practice with accountable talk, teachers can observe the discussions that are taking place and continue modeling based on what students need to improve on.

**Step 4: It’s time to start talking about math, but remember these important strategies**

• Not all questions will lend themselves well to students having a discussion with a partner(s). Having students discuss high level questions will lead to quality thinking and learning.

o Example: The product is 42, what are possible factors? Justify your thinking in pictures or words

o Non-Example: What is the product of 7 and 6?

• Allow students to have wait time before they discuss. This will give students a chance to process the question and will give them more confidence in communicating their thinking and responding to their partner. Wait time can include thinking and/or jotting key points about what they want to discuss in their journals.

• Hold students accountable during their discussion by walking around and listening. After the discussion, students can be held accountable by explaining what their partner said to the class and reflecting on what they learned during the discussion.

• While students are discussing and you are walking around, listen for thinking that all students in the class need to hear to help the class reach the learning goal of the lesson. Highlight excellent thinking by calling on those students to share with the class.

• Use talk moves during whole class discussions that will continue to hold students accountable. For example, after a student shares an important thought that you want to be sure the whole class hears, have another students repeat what they said. Watch this video for more information about talk moves.

For more information about accountable talk in the math class, read this article from Math Solutions. Also, don’t forget to visit your Building Math Community resource located on your Year at a Glance for each grade to get more ideas on Accountable Talk and how to get it started in your math classroom.

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